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Question
`(sin 35^circ/cos 55^circ)^2 + (cos 43^circ/sin 47^circ)^2 - 2 cos 60^circ` = ______.
Fill in the Blanks
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Solution
`(sin 35^circ/cos 55^circ)^2 + (cos 43^circ/sin 47^circ)^2 - 2 cos 60^circ` = 1.
Explanation:
`(sin 35^circ/cos 55^circ)^2 + (cos 43^circ/sin 47^circ)^2 - 2 cos 60^circ`
= `[(sin(90^circ - 55^circ))/(cos 55^circ)]^2 + [(cos(90^circ - 47^circ))/cos 47^circ]^2 - 2 cos 60^circ`
= `((cos 55^circ)/(cos 55^circ))^2 + ((sin 47^circ)/(sin 47^circ))^2 - 2 cos 60^circ`
= `(1)^2 + (1)^2 - 2 xx 1/2`
= 1 + 1 – 1
= 1
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